Which is the correct way to model the equation 5 x + 6 = 4 x + (negative 3) using algebra tiles?

Question

5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
6 positive x-tiles and 5 positive unit tiles on the left side; 3 negative x-tiles and 4 positive unit tiles on the right side
5 positive x-tiles and 6 negative unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side
5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 positive unit tiles on the right side

Answer 1

To model the equation \( 5x + 6 = 4x - 3 \) with algebra tiles, we should correctly interpret each term in the equation.

1. Left side of the equation \(5x + 6\):

   • This means we need 5 positive x-tiles (to represent the \(5x\)) and 6 positive unit tiles (to represent the \(+6\)).

2. Right side of the equation \(4x - 3\):

   • Here, we have 4 positive x-tiles (to represent the \(4x\)) and 3 negative unit tiles (to represent the \(-3\)).

Given this interpretation, we can match it to the options provided:

• Correct modeling: \( 5 \) positive x-tiles and \( 6 \) positive unit tiles on the left side; \( 4 \) positive x-tiles and \( 3 \) negative unit tiles on the right side.

Therefore, the correct answer is:

5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side.